LAST NAME:……………………………………………………… First Name:………………………………………………………… DATE: Wednesday May 20, 2020: 3 Hours (Online) Spring 2020 PHYS 120 Final Instructions: • Show all work to receive full credit. Answers with insufficient supporting work will receive little or no credit. • Please enter your answer int the space provided. • Please BOX your FINAL ANSWER. • Keep 4 significant figures EVERYWHERE!!!! “Physics is much too hard for physicists”, David Hilbert (Mathematician). Page # 2 3 4 5 6 7 8 9 10 Question 1 2 3 4 5 6 7 8 9 # Maximum 14 16 10 10 10 10 10 10 10 Points Student Score 1 Total Points Possible 100 1. [14 Points] Keep 4 significant figures everywhere! A block of mass 𝑀 = 1.5 kg is pushed up an incline with a force 𝐹 = 15 N for a distance 𝑑 = 3 m along the incline, as shown. The angle of the incline is 𝜃 = 36.9°. There is friction between the incline and the block and the coefficient of kinetic friction is 𝜇𝑘 = 0.25. As usual, we take the 𝑥−direction to be along the incline and the 𝑦−direction to be perpendicular to the incline, as shown in the picture. a. Draw ALL the forces on the block on the picture shown. (2 pts) b. Calculate the magnitude of the 𝑥−component of the force of gravity. (2 pts) 𝐹𝑔𝑥 = _________________ N c. Calculate the magnitude of the 𝑦−component of the force of gravity. (2 pts) 𝑦 𝐹𝑔 = _________________ N d. Calculate the normal force. (2 pts) 𝐹𝑁 = ______________ N e. Calculate the magnitude of the force of friction as the block is pushed up the incline. (2 pts) 𝑓𝑘 = _______________ N f. Calculate the acceleration of the block along the incline. (2 pts) 𝑚 𝑎 = _______________ 𝑠2 g. If the block is initially at rest, what is the speed of the block after it is pushed for 3 meters along the incline? (2 pts) 𝑣 = ________________ m/s 2 2. [16 Points] This is a continuation of the previous problem… a. When the block is pushed for 3 meters, how much time has passed? (2 pts) 𝑡 = ______________ s b. Calculate the kinetic energy of the block once it has been pushed for 3 meters. (2 pts) 𝐾𝐸 = _____________ J c. Calculate the work done by the force 𝐹 after the block has been pushed for 3 meters. (2 pts) 𝑊𝐹 = _______________ J d. Calculate the work done by friction after the block has been pushed for 3 meters. (2 pts) 𝑊𝑓𝑘 = ________________J e. Calculate the work done by gravity after the block has been pushed for 3 meters. (2 pts) 𝑊𝑔 = __________________J f. Calculate the work done by the normal force after the block has been pushed for 3 meters. (2 pts) 𝑊𝐹𝑁 = __________________J g. Calculate the work done by all the forces combined after the block has been pushed for 3 meters. (2 pts) 𝑊𝑡𝑜𝑡𝑎𝑙 = __________________J h. Use the total work you just calculated along with the work energy principle to find the speed of the block after it has been pushed for 3 meters. (2 pts) 𝑣 = ____________________ m/s 3 3. [10 Points] A block of mass 𝑀1 = 3 kg is initially at rest on a frictionless surface. The block is then pushed horizontally to the right with a force 𝐹 = 12 𝑁 for 5 seconds. After the push, the block is left to slide with no force applied to it. The block then encounters another block of mass 𝑀2 = 2 kg and the collide inelastically and stick together. After the two blocks collide, the encounter a spring of force constant 𝑘 = 1500 N/m. Once the blocks collide with the spring, they stick to the spring and they oscillate back and forth in simple harmonic motion. a. Find the momentum of the block of mass 𝑀1 after it has been pushed for 5 seconds. (2 pts) 𝑝1 = _______________ kgm/s b. After the two blocks collide and stick together, what is their speed after the collision? (2 pts) 𝑣 = ______________ m/s c. What is the maximum compression of the spring after the two blocks collide with it? (2 pts) 𝐴 = ________________ m d. After the masses collide and stick to the spring, calculate the angular frequency of oscillations. (2 pts) 𝜔 = ___________________ rad/s e. What is the speed of the attached mass when the spring is stretched by 0.35 m? (2 pts) 𝑣 = _____________ m/s 4 4. [10 Points] A beam of uniform mass 𝑚 and length 𝐿 = 3 meters is placed on a pivot a distance 𝑑 = 1 meter from its left end. To keep the beam horizontal and balanced, a mass 𝑀 = 50 kg is placed on the beam at its left end, as shown in the figure. The beam is in static equilibrium. a. Calculate the mass of the beam. (5 pts) 𝑚 = ______________ kg b. If the mass on the left is removed, the beam will start to rotate clockwise and fall down. If the 1 moment of intertia of the beam about the pivot point is 𝐼 = 𝑚𝐿2 , calculate the angular 9 acceleration of the beam immediately after the mass 𝑀 on the left is removed and the beam starts to rotate. (5 pts) 𝛼 = _________________ rad/s2 5 1 5. [10 Points] A copper flask (𝛽𝑐𝑜𝑝𝑝𝑒𝑟 = 51 × 10−6 ℃ ) with a volume of 500 cm3 contains 490 cm3 of 1 olive oil (𝛽𝑜𝑖𝑙 = 0.68 × 10−3 ℃) at a temperature 𝑇0 = 20 ℃. a. To what temperature must the flask and the oil be heated so that the flask will be completely filled? (6 pts) 𝑇 = _________________ ℃ b. Calculate the volume of the copper flask when the temperature is equal to that you calculated in part (a). (2 pts) 𝑉𝑐𝑢 = _________________ cm3 c. Calculate the volume of the olive oil when the temperature is equal to that you calculated in part (a). (2 pts) 𝑉𝑜𝑖𝑙 = _________________ cm3 6 6. [10 Points] A piece of ice having a mass of 2 kg and an initial temperature of −272 ℃ (very cold!) is dropped into a container of water at 25 °C. Remember that: 𝐽 The specific heat of water is 𝑐𝑤 = 4186 𝑘𝑔℃, 𝐽 The specific heat of ice is 2100 𝑘𝑔℃ The latent heat of fusion for water is 𝐿𝐹 = 333000 𝐽 . 𝑘𝑔 a. Very soon after the piece of ice was dropped into the water, all the water froze into ice at 0 ℃. What was the mass of the water the container? (5 pts) 𝑚𝑤 = ____________ kg b. Suppose now we drop that same ice cube (same mass same temperature) into a container that has 1 kg of water at 25 °C. All the water will freeze and become ice. What is the final temperature of the ice? (5 pts) 𝑇 = _____________ ℃ 7 7. [10 Points] A 1 mol of ideal gas undergoes the four-part process shown in the sketch, connecting states A and B. The four parts of the process are labeled 1, 2, 3, and 4. a. Calculate the work done during part 1 of the process (𝑊𝐴→𝐵 ). (2 pts) 𝑊1 = ______________ J b. Calculate the work done during part 2 of the process (𝑊𝐵→𝐶 ). (2 pts) 𝑊2 = ______________ J c. Calculate the work done during part 3 of the process (𝑊𝐶→𝐷 ). (2 pts) 𝑊3 = _______________ J d. Calculate the work done during part 4 of the process (𝑊𝐷→𝐸 ). (2 pts) 𝑊4 = ________________ J e. Find the total work done by the gas during this four-step process (i.e. in going from state A to state E). (2 pts) 𝑊𝐴→𝐸 = _____________ J 8 8. [10 Points] This is a continuation of Problem 7…. a. What is the temperature of the gas at state B? (2 pts) 𝑇𝐵 = _____________ K b. What is the temperature of the gas at state D? (2 pts) 𝑇𝐷 = _____________ K c. What is the change in the internal energy of the gas in going from state B to state D? (3 pts) Δ𝑈𝐵→𝐷 =______________ J d. How much heat is absorbed by the gas in going from state B to state D? (3 pts) 𝑄𝐵→𝐷 = ________________J 9 9. [10 Points] An ideal heat pump is used to heat a room that is at 300 K. The 𝑇𝐻 outdoor temperature is 263 K. Recall that for a heat pump, 𝐶𝑂𝑃𝑖𝑑𝑒𝑎𝑙 = 𝑇 −𝑇 . 𝐻 𝐿 a. If the 𝑊 = 300 J, calculate the heat pumped into the room. (2 pts) 𝑄𝐻 =______________ J b. Calculate the heat extracted from the outside air. (1 pts) 𝑄𝐿 = _____________J c. Calculate the entropy change in the outside air. (2 pts) Δ𝑆𝑜𝑢𝑡 = ____________ J/K d. Calculate the entropy change in the inside air. (2 pts) Δ𝑆𝑖𝑛 = ____________ J/K e. How does Δ𝑆𝑖𝑛 compare with Δ𝑆𝑜𝑢𝑡 ? Are you surprised? Is this consistent with the Second Law of Thermodynamics? An answer consisting of 5 to 10 sentences is enough. (2 pts) ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… ……………………………………………………………………………………………………… f. If the heat pump reversed, it will act as an air conditioner. Calculate the coefficient of this air conditioner. (1 pts) 𝐶𝑂𝑃 = _____________ 10
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